If 24 is the number of standard classrooms, what does $x$ have to represent so that $24x$ gives a total number of seats? Use the same idea for 6 and $y$.

Once you know what $6y$ represents, ask yourself: is $y$ itself a total amount across all lecture halls, or an amount for one lecture hall?

The equation is $24x + 6y = 960$.

• The problem states there are 24 standard classrooms and 6 lecture halls.
• So the coefficient 24 matches the 24 standard classrooms, and the coefficient 6 matches the 6 lecture halls.

That means:

• $24x$ must represent the total seats in the standard classrooms.
• $6y$ must represent the total seats in the lecture halls.

If $24x$ is the total number of seats in the 24 standard classrooms, then $x$ must be the number of seats in each standard classroom (a per-classroom amount).

In general, when a total is written as $k$ times a variable (for example, $6y$), the variable represents the per-item amount. Keep that in mind for the lecture halls term; we will select the matching answer in the next step.

We found that $y$ is the number of seats in each lecture hall, not a total and not for standard classrooms.

So the best interpretation of $y$ is the average number of seats per lecture hall.